GDP Preliminary: We first introduce some background about GDP.
Let \(P\)  and \(Q\)  denote the distributions of \(M(X)\)  and \(M\left(X^{\prime }\right)\)  with \(X\sim X^{\prime }\) , and let \(\phi \)  be any (possibly randomized) rejection rule for testing \(H_{0}: P\)  against \(H_{1}: Q\) . With these in place, [1]} defines the trade-off function of \(P\)  and \(Q\)  as
\(\begin{aligned}\text{T}(P, Q):[0,1] & \mapsto [0,1] \\\alpha & \mapsto \inf _{\phi }\left\lbrace 1-\mathbb {E}_{Q}[\phi ]: \mathbb {E}_{P}[\phi ] \leqslant \alpha \right\rbrace .\end{aligned}\) 
